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On Quantum Fokker–Planck Equation
Journal of Statistical Physics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2014
Abstract This chapter deals with deriving Fokker–Planck equations (FPEs) that govern the behaviour of phase space distribution functions (normalised and unnormalised) for boson and fermion systems due to dynamical or thermal evolution.
Bryan J. Dalton +2 more
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Abstract This chapter deals with deriving Fokker–Planck equations (FPEs) that govern the behaviour of phase space distribution functions (normalised and unnormalised) for boson and fermion systems due to dynamical or thermal evolution.
Bryan J. Dalton +2 more
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American Journal of Physics, 1963
The Fokker-Planck approximation to the interaction term in the Boltzmann transport equation is discussed. For the case of binary collisions a simple derivation of this term is presented. The resultant expressions for the associated quantities 〈Δvi〉 and 〈ΔviΔvi〉 are evaluated for the case of a fully ionized gas.
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The Fokker-Planck approximation to the interaction term in the Boltzmann transport equation is discussed. For the case of binary collisions a simple derivation of this term is presented. The resultant expressions for the associated quantities 〈Δvi〉 and 〈ΔviΔvi〉 are evaluated for the case of a fully ionized gas.
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On symmetries of the Fokker–Planck equation
Journal of Engineering Mathematics, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fokker–Planck–Kolmogorov Equations with a Parameter
Doklady Mathematics, 2023For Fokker–Planck–Kolmogorov equations with coefficients depending measurably on a parameter we prove the existence of solutions that are measurable with respect to this parameter.
Bogachev, V. I., Shaposhnikov, S. V.
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2016
In this chapter, we review the Bakry–Emery approach from the PDE viewpoint (Sect. 2.1) and the original stochastic viewpoint (Sect. 2.3) and detail some known relations to convex Sobolev inequalities (Sect. 2.2). Our focus is the PDE viewpoint addressed by (Toscani, G, Entropy production and the rate of convergence to equilibrium for the Fokker-Planck ...
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In this chapter, we review the Bakry–Emery approach from the PDE viewpoint (Sect. 2.1) and the original stochastic viewpoint (Sect. 2.3) and detail some known relations to convex Sobolev inequalities (Sect. 2.2). Our focus is the PDE viewpoint addressed by (Toscani, G, Entropy production and the rate of convergence to equilibrium for the Fokker-Planck ...
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2021
Diffusion processes, which we introduced in Sec. 4.2.2, can be regarded as generalizations of the fundamental physical process of diffusion. The Fokker–Planck equation is, in turn, the fundamental partial differential equation for the conditional probability relevant to diffusion processes.
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Diffusion processes, which we introduced in Sec. 4.2.2, can be regarded as generalizations of the fundamental physical process of diffusion. The Fokker–Planck equation is, in turn, the fundamental partial differential equation for the conditional probability relevant to diffusion processes.
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1984
As shown in Sects. 3.1, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (3.1, 31). For nonlinear Langevin equations (3.67, 110) expectation values are much more difficult to obtain, so here we first try to derive an equation for the distribution function.
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As shown in Sects. 3.1, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (3.1, 31). For nonlinear Langevin equations (3.67, 110) expectation values are much more difficult to obtain, so here we first try to derive an equation for the distribution function.
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2019
In this chapter we derive the one-dimensional Fokker-Planck equation, which defines the change of the probability of a state variable x in dependence of time, i.e., \( \frac{dP\left(x;t\right)}{dt} \). Starting from the Gaussian normal distribution, we formulate the deterministic drift term of the equation, which can be illustrated by the potential ...
Wolfgang Tschacher, Hermann Haken
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In this chapter we derive the one-dimensional Fokker-Planck equation, which defines the change of the probability of a state variable x in dependence of time, i.e., \( \frac{dP\left(x;t\right)}{dt} \). Starting from the Gaussian normal distribution, we formulate the deterministic drift term of the equation, which can be illustrated by the potential ...
Wolfgang Tschacher, Hermann Haken
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1996
The Fokker-Planck equation was originally developed as an alternative to the Langevin equation as a model of Brownian motion. Obukhov (1959) made the pioneering suggestion that the Fokker-Planck equation be used as a model of turbulent diffusion, but those who followed his suggestion from the 1960s into the 1980s chose to use the Langevin equation ...
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The Fokker-Planck equation was originally developed as an alternative to the Langevin equation as a model of Brownian motion. Obukhov (1959) made the pioneering suggestion that the Fokker-Planck equation be used as a model of turbulent diffusion, but those who followed his suggestion from the 1960s into the 1980s chose to use the Langevin equation ...
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